# LaTeX in WordPress

A proof of the irrationality of $\sqrt{2}$ just to try $\LaTeX$ in WordPress

Assume $\sqrt{2}$ is rational.

Then $\exists a$ and $b$ such that $\sqrt{2} = \frac{a}{b}$
where $a$ and $b$ are integers and $\frac{a}{b}$ is in lowest terms.

$\Rightarrow 2b^2 = a^2$

$\Rightarrow a^2$ is even

$\Rightarrow a$ is even

$\Rightarrow a$ is divisible by $2$

$\Rightarrow \exists k$ such that $a = 2k$

substitute $2k$ for $a$ in the assumption to get
$\sqrt{2} = \frac{2k}{b}$

$\Rightarrow 2 = \frac{(2k)^2}{b^2} = \frac{4k^2}{b^2}$

$\Rightarrow 2k^2 = b^2$

$\Rightarrow b$ is even, similarly.

$\Rightarrow \frac{a}{b}$ is not in lowest terms. $\blacksquare$

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Posted in Mathematics